# Digital SAT Math: Systems of two linear equations in two variables- Practice Questions

## SAT MAth Practice questions – all topics

• Algebra Weightage: 35%  Questions: 13-15
• Linear equations in one variable
• Linear equations in two variables
• Linear functions
• Systems of two linear equations in two variables
• Linear inequalities in one or two variables

## SAT MAth and English  – full syllabus practice tests

[Calc]  Question   Easy

\begin{aligned} & y<x \\ & x>7 \end{aligned}

What point $$(x, y)$$ is a solution to the given system of inequalities in the $$x y$$ plane?
A) $$(0,1)$$
B) $$(3,2)$$
C) $$(6,7)$$
D) $$(9,8)$$

Ans:D

The given system of inequalities is:

\begin{aligned} & y < x \\ & x > 7 \end{aligned}

We need to find the point $$(x, y)$$ that satisfies both inequalities.

Let’s evaluate the given options:

A) $$(0, 1)$$
$$0 > 7$$ (False)
$$1 < 0$$ (False)
This point does not satisfy $$x > 7$$.

B) $$(3, 2)$$
$$3 > 7$$ (False)
$$2 < 3$$ (True)
This point does not satisfy $$x > 7$$.

C) $$(6, 7)$$
$$6 > 7$$ (False)
$$7 < 6$$ (False)
This point does not satisfy $$x > 7$$.

D) $$(9, 8)$$
$$9 > 7$$ (True)
$$8 < 9$$ (True)
This point satisfies both $$x > 7$$ and $$y < x$$.

[No-Calc]  Question Easy

y=18x+25
y =- 14x-7
What is the solution (x,y) to the given system of equations?

A. (-7,25)

B. (-1,7)

C. (7,-1)

D. (25,-7)

Ans: B

To solve this system, we set the equations equal to each other since they both equal $$y$$:
$18x + 25 = -14x – 7$

Now, let’s solve for $$x$$:
$18x + 14x = -7 – 25$
$32x = -32$
$x = -1$

Now that we have $$x = -1$$, let’s find $$y$$ by substituting $$x$$ into one of the original equations. We’ll use the first equation:
$y = 18(-1) + 25$
$y = -18 + 25$
$y = 7$

So, the solution $$(x, y)$$ to the given system of equations is $$(-1, 7)$$, which corresponds to option B).

[Calc]  Question Easy

\begin{aligned} & x=4 \\ & y=\frac{x}{4}+2 \end{aligned}

What is the solution $$(x, y)$$ to the given system of equations?
A) $$(4,6)$$
B) $$(4,3)$$
C) $$(4,2)$$
D) $$(4,1)$$

B

We need to find the solution $$(x, y)$$ to the given system of equations.

First, substitute $$x = 4$$ into the equation for $$y$$:
$y = \frac{4}{4} + 2$
$y = 1 + 2$
$y = 3$

Therefore, the solution to the system of equations is:
$(x, y) = (4, 3)$

$\boxed{B}$

[Calc]  Question  Easy

The table shows the prices of 3 items in a certain store on January $$15,1913$$.

On January 15,1913 , Samuel purchased $$s$$ pounds of sugar and $$p$$ pounds of potatoes for a total of $$\ 0.16$$. The total weight of the purchase was 4 pounds. Based on the prices in the table, which system of equations represents this situation?

A) $$0.06 s+0.02 p=0.16$$
$$s+p=4$$

B) $$6 s+2 p=0.16$$
$$s+p=4$$

C) $$0.06 s+0.02 \mathrm{p}=4$$
$$s+p=0.16$$

D) $$6 s+2 p=4$$
$$s+p=0.16$$

Ans: A

The total cost of the purchase was $$\ 0.16$$. Therefore, the equation for the cost is:
$0.06 s+0.02 p=0.16$

The total weight of the purchase was 4 pounds. Therefore, the equation for the weight is:
$s+p=4$

Putting these two equations together, the system of equations representing this situation is:
$\left\{\begin{array}{l} 0.06 s+0.02 p=0.16 \\ s+p=4 \end{array}\right.$

[Calc]  Question   Foundation

\begin{aligned} & x=3 \\ & y=x+3 \end{aligned}

What is the solution $$(x, y)$$ to the given system of equations?

A) $$(3,6)$$
B) $$(3,3)$$
C) $$(3,-3)$$
D) $$(3,-6)$$

Ans:A

1. From the first equation, we know:
$x = 3$

2. Substitute $$x = 3$$ into the second equation:
$y = 3 + 3 = 6$

So, the solution to the system of equations is $$(x, y) = (3, 6)$$.

[No-Calc]  Question Easy

In the 1884 US presidential election, candidates James Blaine and Grover Cleveland received a total of 401 electoral college votes. The number of electoral college votes Blaine received, b, was 37 fewer than the number of electoral college votes Cleveland received, c. Which system of equations represents this situation?

A) b + c = 438

b = c – 37

B) b + c = 438

b = c + 37

C) b + c = 401

b = c – 37

D) b + c = 401

b = c + 37

C) b + c = 401

b = c – 37

Translate the given information into a system of equations:

1. Total electoral college votes: The total number of electoral college votes received by Blaine ($$b$$) and Cleveland ($$c$$) is 401.

This can be formulated into two equations:

The sum of the votes for Blaine and Cleveland: $$b + c = 401$$
Blaine received 37 fewer votes than Cleveland: $$b = c – 37$$

Thus, the correct system of equations is:
\begin{aligned} & b + c = 401 \\ & b = c – 37 \end{aligned}

### Question

$$nx+3y=1$$
$$12x-6y=0$$

In the system of equations above, $$n$$ is a constant. If the system has no solution, what is the value of $$n$$  ?

1. -9
2. -6
3. 3
4. 6

Ans: B

### Question

$$3x+2y=8$$
$$4x-3y=5$$

The solution to the given system of equations is $$(xy)$$. What is the value of $$x$$?

Ans: 2

### Question

3$$x$$+4$$y$$=35

2$$x$$+2$$y$$=15

The solution to the given system of equations is ($$x$$,$$y$$). What is the value of $$x$$+2$$y$$ ?

Ans: 20

### Question

4$$x$$+$$y$$=7

2$$x$$-7$$y$$=1

If ($$x$$,$$y$$) is the solution of the given system of equations, what is the value of $$x$$?

Ans: 5/3, 1.66, 1.67

### Question

$$\frac{1}{2}x+5=kx+7$$

In the given equation, $$k$$ is a constant. The equation has no solution. What is the value of $$k$$?

Ans: 1/2, .5

### Question

$$x$$+2$$y$$=10

2$$x$$-$$y$$=5

The solution to the given system of equations is ($$x$$, $$y$$). What is the value of 3$$x$$ + $$y$$ ?

1. 5
2. 7
3. 13
4. 15

Ans: D

### Question

How many solutions does the equation $$|x+7|=-4$$ have?

1. Zero
2. Exactly one
3. Exactly two
4. More than two

Ans: A

Question

.

What system of linear equations is represented by the lines shown? 1.6

1. 3$$x$$-2$$y$$=6
3$$x$$-2$$y$$=12
2. 3$$x$$-2$$y$$=6
3$$x$$+2$$y$$=12
3. 2$$x$$+3$$y$$=6
2$$x$$-3$$y$$=12
4. -2$$x$$-3$$y$$=6
-2$$x$$+3$$y$$=12

A

Question

$$5x + 3y = 31$$
$$5x – 4y = 17$$
If $$(x, y)$$ is the solution to the given system of equations, what is the value of $$10x – y$$ ?

48

Question

The City Transit bus line charges $\$ 2$for an adult and$\$1$ for a child to ride one way. During a certain 4 -hour shift, a bus driver collected $\$ 1,171$from 617 riders. Which of the following systems of equations could be used to determine the number of adult riders,$A$, and the number of child riders,$C, during this 4-hour shift? A. \begin{aligned} & 2 A+C=4(1,171) \\ & A+C=4(617) \end{aligned} B.4(2 A)+4 C=1,1714(A+C)=617C. \begin{aligned} & 2 A+C=617 \\ & A+C=1,171 \\ & 2 A+C=1,171 \\ & A+C=617 \end{aligned} D.2 A+C=1,171A+C=617$▶️Answer/Explanation Ans: D Question The equation$9 x+5=a(x+b)$, where$a$and$b$are constants, has no solutions. Which of the following must be true? I.$a=9$II.$b=5$III.$b \neq \frac{5}{9}$A. None B. I only C. I and II only D. I and III only ▶️Answer/Explanation Ans: D Question$5 x+2 y=224 x+y=17$In the system of equations above, what is the value of$x+y$? A. 5 B. 4 C. 3 D. 2 ▶️Answer/Explanation Ans: A Questions$2 x-y=-4
2 x+y=4
$For the solution of the system of equations above, what is the value of$x$? A. -4 B. -2 C. 0 D. 2 ▶️Answer/Explanation Ans: C Questions The function$g$is defined as$g(x)=\frac{2 x}{3}+3$. What is the value of$g(-30) ?A. -27 B. -23 C. -17 D. -7 ▶️Answer/Explanation Ans: C Questions \begin{aligned} &x+y=21 \\ & x-2 y=-3 \end{aligned} According to the system of equations above, what is the value ofx ?$A. 6 B. 8 C. 13 D. 15 ▶️Answer/Explanation Ans: C Question$3(x+y)=12
\frac{x}{2}=3
$If$(x, y)$is a solution to the system of equations above, what is the value of$y$? A. -6 B. -2 C. 2 D. 6 ▶️Answer/Explanation Ans: B Question A pool initially contains 1,385 cubic feet of water. A pump begins emptying the water at a constant rate of 20 cubic feet per minute. Which of the following functions best approximates the volume$v(t)$, in cubic feet, of water in the pool$t$minutes after pumping begins, for$0 \leq t \leq 69$? A.$v(t)=1,385-20 t$B.$v(t)=1,385-69 t$C.$v(t)=1,385+20 t$D.$v(t)=1,385+69 t\$