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Use substitution to solve each system of equations. 4x+y=10 2.

Question

Use substitution to solve each system of equations. 4x+y=10 2.

Use substitution to solve each system of equations.
4x+y=10
2.

Solution

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AniyaMaster · Tutor for 5 years

Answer

### This problem is unsolvable as stated because the second equation is missing. *If* the second equation were $2x - 3y = 22$, then the solution would be $(\frac{26}{7}, -\frac{34}{7})$.

Explain

## Step 1: Isolate a variable.<br />### The first equation, $4x + y = 10$, can be easily rearranged to isolate $y$: Subtract $4x$ from both sides to get $y = 10 - 4x$.<br /><br />## Step 2: Substitute and solve.<br />### Substitute the expression for $y$ from Step 1 into the second equation (which is missing, making the problem unsolvable as presented). *Assuming* the second equation was $2x - 3y = 22$, the substitution would look like this: $2x - 3(10 - 4x) = 22$. Simplifying this gives $2x - 30 + 12x = 22$, which further simplifies to $14x = 52$, and finally $x = \frac{52}{14} = \frac{26}{7}$.<br /><br />## Step 3: Solve for the other variable.<br />### Substitute the value of $x$ back into either of the original equations. Using the first equation: $4(\frac{26}{7}) + y = 10$. This simplifies to $\frac{104}{7} + y = 10$. Solving for $y$ gives $y = 10 - \frac{104}{7} = \frac{70 - 104}{7} = -\frac{34}{7}$.
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