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
Question Medium
\[
6=\frac{2}{3}(x-7)
\]
Which equation has the same solution as the given equation?
A) \(9=x-14\)
B) \(9=\frac{2}{3} x-7\)
C) \(9=x-7\)
D) \(9=x-\frac{14}{3}\)
▶️Answer/Explanation
Ans:C
Given equation:
\[
6 = \frac{2}{3}(x – 7)
\]
To find an equivalent equation, start by clearing the fraction. Multiply both sides by \(\frac{3}{2}\):
\[
6 \cdot \frac{3}{2} = x – 7
\]
\[
9 = x – 7
\]
So, the equation equivalent to the given equation is:
\[
\boxed{9 = x – 7}
\]
Question medium
$
\begin{aligned}
& 3 x+4 y=18 \\
& 2 x-4 y=17
\end{aligned}
$
The solution to the given system of equations is \((x, y)\). What is the value of \(x\) ?
▶️Answer/Explanation
Ans:7
To solve the given system of equations, we can use the method of elimination.
Given the system:
\[
\begin{align*}
3x + 4y &= 18 \\
2x – 4y &= 17
\end{align*}
\]
We can eliminate \(y\) by adding the equations together:
\[ (3x + 4y) + (2x – 4y) = 18 + 17 \]
\[ 3x + 2x = 35 \]
\[ 5x = 35 \]
\[ x = \frac{35}{5} \]
\[ x = 7 \]
So, the value of \(x\) is \(7\).
Question medium
$
\begin{aligned}
& y=4 x+1 \\
& y=4 x+3
\end{aligned}
$
How many solutions does the given system of equations have?
A. Zero
B. Exactly one
C. Exactly two
D. Infinitely many
▶️Answer/Explanation
Ans:A
The given system of equations is:
\[
\begin{align*}
y &= 4x + 1 \\
y &= 4x + 3 \\
\end{align*}
\]
These are two parallel lines with the same slope \(4\). Since they have the same slope but different intercepts, they will never intersect. Therefore, the system has zero solutions, which corresponds to option A: Zero.
Question medium
$
\begin{gathered}
y=4 x+6 \\
-5 x-y=21
\end{gathered}
$
What is the solution \((x, y)\) to the given system of equations?
A. \((-3,-6)\)
B. \(\left(-\frac{5}{3},-\frac{2}{3}\right)\)
C. \((3,18)\)
D. \((15,66)\)
▶️Answer/Explanation
Ans:A
To solve the system of equations:
\[
\begin{gathered}
y=4x+6 \\
-5x-y=21
\end{gathered}
\]
We can use substitution or elimination method. Let’s use the substitution method:
From the first equation, we have \(y = 4x + 6\). Substitute this expression for \(y\) into the second equation:
\[-5x – (4x + 6) = 21\]
\[-5x – 4x – 6 = 21\]
\[-9x – 6 = 21\]
Now, add 6 to both sides:
\[-9x = 27\]
Divide both sides by -9:
\[x = -3\]
Now, substitute \(x = -3\) back into one of the equations to find \(y\):
\[y = 4(-3) + 6\]
\[y = -12 + 6\]
\[y = -6\]
So, the solution to the system of equations is \((-3, -6)\), which corresponds to option A.
Question medium
$
|x-10|=0
$
What are all possible solutions to the given equation?
A. -10
B. 0
C. 10
D. -10 and 10
▶️Answer/Explanation
Ans:C
The equation \(|x – 10| = 0\) implies that the expression inside the absolute value must be equal to 0 for the equation to be true. So,
\[x – 10 = 0\]
\[x = 10\]
Thus, the only possible solution is \(x = 10\), which corresponds to option C.